@In_die_bos,
You've received a lot of good information here and I won't bother to repeat it. I will say when I started load dev't on my .375 M70, I found it didn't care that much for Varget or it's virtual twin RL15. Many 375 owners have found good loads with these powders.
What I found worked very well with 300gr pills is IMR4350. It works well with North Fork bonded cores, Swift A-Frames and the Barnes TSX.
But it was with the Barnes TSX I found they are sensitive to copper fouling. If you're going to use these, I recommend you clean your barrel very thoroughly. As copper free as you can get within reason. Once you do this, retry your Barnes load that you had some success with early on. And also of course once you're certain screws are tight and you don't have a broken scope.
What I have found in my 375 and other rifles is that once the copper builds up enough, accuracy will drop off and drop off fast with subsequent shots. Clean the barrel again and the accuracy will return. I am not the only one in this world that has seen this. I picked up that this might be the problem for me after reading a number of reports of this issue with Barnes.
As you're shooting these, take time to inspect the crown and that end of the barrel that you can see into. What you're looking for is that copper build up coming off the bullets. If your experience is similar to mine, you will notice your barrel there going from black/grey to the same color as your bullets. While doing this of course keep track of how many rounds you've put down range.
For my rifle, somewhere around 8-10 rounds is when the accuracy started to drop off. This issue is I believe a function of the copper Barnes uses as well as the barrel. A tighter barrel and the build up will happen sooner and you'll see the accuracy problem that much sooner. A looser barrel and you may never see the issue as you clean the barrel before it ever becomes a problem.